, Volume 163, Issue 1, pp 1-24
Date: 19 Oct 2005

Correlations for pairs of closed geodesics

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Abstract

In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems have been studied in both Quantum Chaos and number theory.